Answer

Flaffy11 to the rescue!

Hello! Like 'yoshi114' said, you can't get the pokemon flute in this generation.
Originally, the poke - flute was used to wake two sleeping snorlaxs up which are blocking
a path. So the poke – flute can be found in lavender town in pokemon blue, pokemon red,
pokemon green and pokemon yellow: pikachu special edition. Hope this helped,
Flaffy11

No Poke Flute, but has some other Flute

In pokemon emerald, there's no poke flute... But you can get blue flute, red flute, yellow
flute, black flute and white flute, in fallarbor town... Each of those flutes has their
different effects, healing certain conditions...

here are some flutes tht are almost the same thing as the poke flute and how to get them

U go to fallarbur town and theres a house there called the glass workshop u just talk to
the man in there and he gives u a bag to store your ash, u get ash by walking through the
ash covered grass surrounding the house, then u go back in the house and talk to the man
again, he gives u a option list and if have enough ash he blows things for u including
different types of flutes tht restore pokemon with disabilities like burned, poisining,
frozen, and sleep

go to glass workshop in fallabor town

Go to fallabor town, and when you first get there there's all this ash raining down all
over the place, and after you've gotten to the end of the ashy field you will see a house.
Inside is the glass workshop man, talk to him and he'll give you special rewards if you
collect ash for him. It's not the pokefulte, you can;t get it in pokemon emerald version,
but it;s like yellow, white, and some otther flute...